2 Answers
2

You should be doing periodic backups and restores to test your restore procedures, but as far as doing them to improve performance, you can rebuild indexes and shrink files with Maintenance Plans, which is the preferred method.

Backups/Restores are carried out at byte level - they have no affect on fragmentation in the database.
Restores should be done regularly to make sure you are confidant in how the process goes (including getting the system attached to the restored database) and that the backups are proved to be usable. Your other answer is correct in saying that index maintenance is a separate process you need to carry out.